Ultrasonic characterization of functionally graded materials using a continuously graded model and spectral inversion

Area of Science:

• Materials Science
• Acoustics
• Computational Mechanics

Background:

• Quantitative ultrasonic characterization of functionally graded materials (FGMs) is hindered by conventional discrete layered models (DLMs).
• DLMs approximate continuous gradients as sharp interfaces, introducing non-physical spectral features and inaccurate results.
• Accurate characterization is crucial for optimizing FGM performance in demanding applications.

Purpose of the Study:

• To develop a physically consistent continuously graded model (CGM) for ultrasonic wave propagation in FGMs.
• To integrate the CGM with particle swarm optimization (PSO) for accurate estimation of FGM layer thicknesses.
• To validate the proposed CGM-PSO framework experimentally.

Main Methods:

• Development of a continuously graded model (CGM) accounting for smooth variations in acoustic impedance.
• Application of particle swarm optimization (PSO) to invert ultrasonic reflection coefficient spectra (URCS) for layer thickness.
• Sensitivity analysis to identify informative spectral features (resonance troughs) for thickness inversion.
• Experimental validation using a three-layer Tungsten-Copper/Silicon Carbide (W-Cu/SiC) FGM.

Main Results:

• The CGM effectively reduces artificial interface reflections compared to DLMs.
• Sensitivity analysis confirmed resonance troughs in URCS are key for thickness inversion.
• Experimental results demonstrated accurate layer thickness estimation with relative errors below 6% using the CGM-PSO framework.
• The method showed robustness even with significant deviations in initial parameter guesses.

Conclusions:

• The developed CGM-PSO framework offers a physically consistent and accurate method for ultrasonic characterization of FGMs.
• This approach overcomes limitations of discrete models, enabling reliable quantitative analysis of continuously graded structures.
• The findings pave the way for improved non-destructive evaluation and quality control of FGMs.